Pions and kaons from

stringy quark matter

T.S.Bíró and K.Ürmössy,

MTA KFKI RMKI Budapest, Hungary

• String model, string distribution

• EoS with stringy interaction

• Coalescense from stringy matter

• Pion and kaon pt spectra

SQM 2008, Peking, China.

Statistical Model

How can be E / N = 6 T ?

Massive hadrons (rho?)

How can be E / N = 6 T ?

Statistical Model: hadronization point around µ = 0 (RHIC, LHC)

How can be E / N = 6 T ?

Ideal gas of radiation

How can be E / N = 6 T ?

Bag Model for QGP

How can be E / N = 6 T ?Stringy Massless QGP

How can be E / N = 6 T ?Stringy Massless QGP

322331 // nAnngσσn

Biro, Cleymans, 2008

Stringy corrections to QGP

Endline: last possible solution

Boltzmann approximation

T

µ

This branch is given by Lambert’s W

High – T equation of state

31

13144

213

:QCD lattice

~1

313

TcT

A

T

pe

Medium-high-T behavior of lattice eos

2

20

T

m

High-T behavior of lattice eos

Boltzmann approximation

Fodor Katz

High-T behavior of lattice eos

Boltzmann approximation

Fodor Katz

The zero pressure line

St. Mod.

Pressure: NP effects at any T

)(1

)()0(22)(

)()(

)()(

222

2

2

/

00

22

0

2222

T

TfT

pppp

dxxfdQQP

dQQPpdQQPpp

NPpp

T

NPP

If it were f(0) = 0, then the QGP pressure would be free of NP effects!

Thermal distribution of Q²

Q²9T²

1/16T²

Coalescense kinematics with strings

qpp

ppp

pmEEH

221

21

22

21

m

Coalescense: formula

m

mEEE

mgqmC

qpfqpf

H

with

))((

)(),(

)2/()2/(

2

21

2

21

Coalescense factor

)(~

~)(

3

222

3

q

qqC

Coalescense: string mass distribution

d

dd

m

mmmg )1(exp~)( 11

Prejudice: d = 1…3

Biro,Shanenko,Toneev: 1999

Coalescense ratio vs string mass

21

)()()()(

)(

2211EEE

H

HH

H

dmmgEGEfEf

Ef

Prejudice: d = 1…3

Goal: fit the parameters of g(m) from low pt

need for strings at low pt

)()(/)(2211EfEfEfG

HH

π

K

blue: fitted g(m)

π: <m>=0.087, d=1.187; K: <m>=0.121, d=1.595

Inetgrated String-length Distribution

K

π

dmmg )(

π: T=100 MeV, q=1.096; K: T=70 MeV, q=1.102

Comparison with RHIC Spectra

v=0.274

Max:

Antiproton spektrum (RHIC)

Max:

Kaon spektrum (RHIC)

STAR

PHENIX

TK=142MeV qK=1.059

Pion spektrum (RHIC)

Max: no data around mpion

PHENIX

Flows with p-

Flows with Kaon

vflow=0.27Tп1=107MeV

qп1=1.096

qп2=1.096

Tп2=75MeVvflow=0.55

Summary

• Strings give a realistic eos and E / N = 6T

• Above Tc there are non-perturbative

effects

• Coalescence of Tsallis-Pareto distributions

• Strings help the product formula at low pt

• Expect at LHC: same T, different q

If the accumulation of false beliefs is cleared away, Enlightenment will appear.

But, strange enough, when people attain Enlightenment, they will realize that

Without false beliefs there could be no Enlightement.

(The Teaching of Buddha)

Bibliography

• arXiv: 0801.3998, T.S.Biro and J. Cleymans: The hadronization

line in stringy matter

• hep-ph / 98083941, T.S.Biro, P.Levai, J.Zimanyi and C.Traxler:

Hadronization in heavy ion collisions, PRC59, ……, 1999

• T.S.Biro, A.A.Shanenko and V.D.Toneev: Toward Thermodynamic

Consistency of Quasiparticle Picture, Phys.Atomic Nuclei 66, 982, 2003

• J.Cleymans, H.Oeschler, K.Redlich, S.Wheaton, PRC73, 034905, 2006.